1. Field of the Invention
The present invention relates generally to a piezoelectric filter of an energy-trapped type, and more particularly, to a three-terminal piezoelectric filter of an energy-trapped type using a second harmonic wave of the thickness-extensional vibration mode.
2. Description of the Prior Art
FIG. 7 illustrates a conventional double-mode piezoelectric filter of an energy-trapped type using the thickness-extensional vibration mode (referred to as TE mode hereinafter). In this piezoelectric filter, an input electrode 53 and an output electrode 54 are arranged in close proximity on one major surface of a piezoelectric substrate 51 polarized in the direction of thickness. An earth electrode 52 is formed on the other major surface of the piezoelectric substrate 51 so as to be opposed to the input electrode 53 and the output electrode 54. This piezoelectric filter has a structure using a fundamental wave of the TE mode. Arrows in FIG. 7 indicate the direction of polarization.
In the above described conventional piezoelectric filter using the fundamental wave of the TE mode, materials having a Poisson's ratio of 1/3 or more must be used as materials for the piezoelectric substrate so as to achieve energy trapping. More specifically, when the fundamental wave of the TE mode is utilized, dispersion curves vary with the Poisson's ratio of the materials for the piezoelectric substrate, as shown in FIGS. 8A and 8B.
FIG. 8A shows a dispersion curve of the fundamental wave of the TE mode in a case where the materials for the piezoelectric substrate has an (effective) Poisson's ratio of 1/3 or more, and FIG. 8B shows a dispersion curve of the fundamental wave of the TE mode in a case where it has an (effective) Poisson's ratio of less than 1/3. In each of FIGS. 8A and 8B, the axis of ordinate represents a frequency f and the axis of abscissa is a wave number k. The right half of the axis of abscissa indicates a real region of k, and the left half thereof indicates an imaginary region of k. In addition, a solid line Q is a dispersion curve in a no-electrode portion provided with no input and output electrodes and no earth electrode, and a broken line R is a dispersion curve in an electrode portion having electrodes formed on its surface. In the electrode portion, the dispersion curve is shifted to a lower frequency side due to the piezoelectric reaction and the mass load effect of the electrodes. Accordingly, a cut-off frequency f.sub.11 of the fundamental wave in the electrode portion is lower than a cut-off frequency f.sub.10 of the fundamental wave in the no-electrode portion (f.sub.11 &lt;f.sub.10).
As shown in FIG. 8A, in a case where the Poisson's ratio is 1/3 or more, the wave number k in the electrode portion becomes a real number at frequencies higher than the cut-off frequency f.sub.11, while the wave number k in the no-electrode portion becomes an imaginary number at frequencies lower than the cut-off frequency f.sub.10. Accordingly, at the frequency f in the range of f.sub.11 to f.sub.10, a propagation mode of vibration exists in the electrode portion, while vibration is not propagated in the no-electrode portion, to be damped, thereby to actieve trapping of vibratory energy in the vicinity of the electrode portion.
On the other hand, as shown in FIG. 8B, in a case where the Poisson's ratio is less than 1/3, the wave number k in the electrode portion becomes a real number at frequencies lower than the cut-off frequency f.sub.11, while the wave number k in the no-electrode portion becomes an imaginary number at frequencies higher than the cut-off frequency f.sub.10. Moreover, f.sub.11 &lt;f.sub.10. Accordingly, in this case, there exists no frequency region where the wave number is a real number in the electrode portion and the wave number is an imaginary number in the no-electrode portion, thereby to make it impossible to trap vibratory energy.
Therefore, in the piezoelectric filter using the fundamental wave of the TE mode, piezoelectric materials having an (effective) Poisson's ratio of 1/3 or more such as piezoelectric ceramics of the titanate zirconate (PZT) system must be used so as to achieve energy trapping. More specifically, materials usable for the piezoelectric substrate are limited. Consequently, even if there exist materials favorable as the materials for the piezoelectric substrate such as piezoelectric materials superior in temperature characteristics, materials high in Q, materials low in loss or materials large in attenuation amount, the materials cannot be employed if the Poisson's ratio thereof is less than 1/3. Accordingly, it is difficult to construct a filter or the like having substantially superior characteristics.
Furthermore, the thickness of a device of the piezoelectric filter having a structure shown in FIG. 7 may be reduced so as to heighten the frequency at which the piezoelectric filter is used. If the device is caused to be usable in a high frequency region, however, the thickness of the device becomes too small, thereby to make it difficult to process and handle the device in the manufacturing processes. Consequently, the conventional piezoelectric filter has a limit in heightening the frequency at which the piezoelectric filter is used.